Pub. Date:
Springer-Verlag New York, LLC
Particle Accelerator Physics II: Nonlinear and Higher-Order Beam Dynamics

Particle Accelerator Physics II: Nonlinear and Higher-Order Beam Dynamics

by Helmut Wiedemann


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Product Details

ISBN-13: 9783540575641
Publisher: Springer-Verlag New York, LLC
Publication date: 05/28/1995
Pages: 480
Product dimensions: 6.50(w) x 1.50(h) x 9.50(d)

Table of Contents

1. Hamiltonian Formulation of Beam Dynamics.- 1.1 Hamiltonian Formalism.- 1.1.1 Lagrange Equations.- 1.1.2 Hamiltonian Equations.- 1.1.3 Canonical Transformations.- 1.1.4 Action-Angle Variables.- 1.2 Hamiltonian Resonance Theory.- 1.2.1 Nonlinear Hamiltonian.- 1.2.2 Resonant Terms.- 1.2.3 Resonance Patterns and Stop-Band Width.- 1.2.4 Third-Order Resonance.- 1.3 Hamiltonian and Coupling.- 1.3.1 Linearly Coupled Motions.- 1.3.2 Higher-Order Coupling Resonances.- 1.3.3 Multiple Resonances.- 1.4 Symplectic Transformation.- Problems.- 2. General Electromagnetic Fields.- 2.1 General Transverse Magnetic-Field Expansion.- 2.2 Third-Order Differential Equation of Motion.- 2.3 Periodic Wiggler Magnets.- 2.3.1 Wiggler Field Configuration.- 2.3.2 Focusing in a Wiggler Magnet.- 2.3.3 Hard-Edge Model of Wiggler Magnets.- 2.4 Superconducting Magnet.- Problems.- 3. Dynamics of Coupled Motion.- 3.1 Conjugate Trajectories.- 3.2 Particle Motion in a Solenoidal Field.- 3.3 Transverse Coupled Oscillations.- 3.3.1 Equations of Motion in Coupling Systems.- 3.3.2 Coupled Beam Dynamics in Skew Quadrupoles.- 3.3.3 Equations of Motion in a Solenoid Magnet.- 3.3.4 Transformation Matrix for a Solenoid Magnet.- 3.3.5 Betatron Functions for Coupled Motion.- Problems.- 4. Higher-Order Perturbations.- 4.1 Kinematic Perturbation Terms.- 4.2 Control of the Central Beam Path.- 4.3 Dipole Field Errors and Dispersion Function.- 4.4 Dispersion Function in Higher Order.- 4.4.1 Chromaticity in Higher Approximation.- 4.4.2 Nonlinear Chromaticity.- 4.5 Perturbation Methods in Beam Dynamics.- 4.5.1 Periodic Distribution of Statistical Perturbations.- 4.5.2 Statistical Methods to Evaluate Perturbations.- Problems.- 5. Hamiltonian Nonlinear Beam Dynamics.- 5.1 Higher-Order Beam Dynamics.- 5.1.1 Multipole Errors.- 5.1.2 Nonlinear Matrix Formalism.- 5.2 Aberrations.- 5.2.1 Geometric Aberrations.- 5.2.2 Filamentation of Phase Space.- 5.2.3 Chromatic Aberrations.- 5.2.4 Particle Tracking.- 5.3 Hamiltonian Perturbation Theory.- 5.3.1 Tune Shift in Higher Order.- Problems.- 6. Charged Particle Acceleration.- 6.1 Accelerating Fields in Resonant rf Cavities.- 6.1.1 Wave Equation.- 6.1.2 Waveguide Modes.- 6.1.3 rf Cavities.- 6.1.4 Cavity Losses and Shunt Impedance.- 6.1.5 Determination of rf Parameters.- 6.2 Beam-Cavity Interaction.- 6.2.1 Coupling Between rf Field and Particles.- 6.2.2 Beam Loading and rf System.- 6.2.3 Higher-Order Mode Losses in an rf Cavity.- 6.2.4 Beam Loading in Circular Accelerators.- 6.3 Higher-Order Phase Focusing.- 6.3.1 Path Length in Higher Order.- 6.3.2 Higher-Order Phase Space Motion.- 6.3.3 Stability Criteria.- 6.4 FODO Lattice and Acceleration.- 6.4.1 Transverse Beam Dynamics and Acceleration.- 6.4.2 Adiabatic Damping.- Problems.- 7. Synchrotron Radiation.- 7.1 Theory of Synchrotron Radiation.- 7.1.1 Radiation Field.- 7.2 Synchrotron Radiation Power and Energy Loss.- 7.3 Spatial Distribution of Synchrotron Radiation.- 7.4 Synchrotron Radiation Spectrum.- 7.4.1 Radiation Field in the Frequency Domain.- 7.4.2 Spectral Distribution in Space and Polarization.- 7.4.3 Angle-Integrated Spectrum.- Problems.- 8. Hamiltonian Many Particle Systems.- 8.1 The Vlasov Equation.- 8.1.1 Betatron Oscillations and Perturbations.- 8.1.2 Damping.- 8.2 Damping of Oscillations in Electron Accelerators.- 8.2.1 Damping of Synchrotron Oscillations.- 8.2.2 Damping of Vertical Betatron Oscillations.- 8.2.3 Robinson’s Damping Criterion.- 8.2.4 Damping of Horizontal Betatron Oscillations.- 8.3 The Fokker-Planck Equation.- 8.3.1 Stationary Solution of the Fokker-Planck Equation.- 8.3.2 Particle Distribution Within a Finite Aperture.- 8.3.3 Particle Distribution in the Absence of Damping.- Problems.- 9. Particle Beam Parameters.- 9.1 Particle Distribution in Phase Space.- 9.1.1 Diffusion Coefficient and Synchrotron Radiation.- 9.1.2 Quantum Excitation of Beam Emittance.- 9.1.3 Horizontal Equilibrium Beam Emittance.- 9.1.4 Vertical Equilibrium Beam Emittance.- 9.2 Equilibrium Energy Spread and Bunch Length.- 9.3 Phase-Space Manipulation.- 9.3.1 Exchange of Transverse Phase-Space Parameters.- 9.3.2 Exchange of Longitudinal Phase-Space Parameters.- 9.4 Polarization of Particle Beam.- Problems.- 10. Collective Phenomena.- 10.1 Statistical Effects.- 10.1.1 Schottky Noise.- 10.1.2 Stochastic Cooling.- 10.1.3 Touschek Effect.- 10.1.4 Intra-Beam Scattering.- 10.2 Collective Self Fields.- 10.2.1 Transverse Self Fields.- 10.2.2 Fields from Image Charges.- 10.2.3 Space-Charge Effects.- 10.2.4 Longitudinal Space-Charge Field.- 10.3 Beam-Current Spectrum.- 10.4 Wake Fields and Impedance.- 10.4.1 Definitions of Wake Field and Impedance.- 10.4.2 Impedances in an Accelerator Environment.- 10.5 Coasting-Beam Instabilities.- 10.5.1 Negative-Mass Instability.- 10.5.2 Dispersion Relation.- 10.5.3 Landau Damping.- 10.5.4 Transverse Coasting-Beam Instability.- 10.6 Longitudinal Single-Bunch Effects.- 10.6.1 Potential-Well Distortion.- 10.7 Transverse Single-Bunch Instabilities.- 10.7.1 Beam Break-Up in Linear Accelerators.- 10.7.2 Fast Head-Tail Effect.- 10.7.3 Head-Tail Instability.- 10.8 Multi-Bunch Instabilities.- Problems.- 11. Insertion Device Radiation.- 11.1 Particle Dynamics in an Undulator.- 11.2 Undulator Radiation.- 11.3 Undulator Radiation Distribution.- 11.4 Elliptical Polarization.- Problems.- References.- Suggested Reading.- Author Index.

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